Patients receive cetuximab intravenously (IV) over 60-120 minutes on days 1, 8, 15, and 22. Treatment with cetuximab repeats every 4 weeks for 2 courses. Beginning in week 2 of course 1, patients undergo concurrent IMRT 5 days per week for 7 weeks. Beginning in week 4 (day 1 of course 2) patients also receive ipilimumab IV over 90 minutes once every 21 days for 3 courses. Treatment continues in the absence of disease progression or unacceptable toxicity. Patients achieving disease progression may undergo surgery after completion of therapy.